How to approach a summation problem with alternating terms?

[mendem03]

I want to know how to start this problem, but don't want the answer.
If someone can just help me get started or give me a tip on how to approach these kinds of questions

 

[Bacle]

Well, just try to see what happens when you add the terms up to a certain term an in your sequence, to get Sn:

S1=1

S2=1+3=4

S3=1+3+5=9



And make a guess, then use induction or some other formula.

What is your guess for Sn=a1+a2+...+an ?

 

[JJacquelin]

1+3+5+...+(2n-5)+(2n-3)+(2n-1) =
= 1+(2n-1) +3+(2n-3) +5+(2n-5)+...
Do you see a simplification ?